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Specification map-ops
enrich
   map+set
with
   functions 
       . .map ( . ) : Map('a, 'b) × ('b → 'c) → Map('a, 'c);
       . .map ( . ) : Map('a, 'b) × ('a × 'b → 'c) → Map('a, 'c);
   
   variables 
       f : 'b → 'c;
       g : 'a × 'b → 'c;
       a : 'a;
       b : 'b;
       c : 'c;
   
   
   axioms 
      map-in: a ∈ st.map(f) ↔ a ∈ st;
      used for: s, ls;
      
      map-at: a ∈ st → st.map(f)[a] = f(st[a]);
      used for: ls;
      
      mapi-in: a ∈ st.map(g) ↔ a ∈ st;
      used for: s, ls;
      
      mapi-at: a ∈ st → st.map(g)[a] = g(a, st[a]);
      used for: ls;
   
   
end enrich